What is the extreme f(x)=2x^3-9x^2-24x ?

The extreme f(x)=2x^3-9x^2-24x is Maximum(-1,13),Minimum(4,-112)

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extreme f(x)=2x^3-9x^2-24x

extreme points

f (x) = 2 x^{3} - 9 x^{2} - 24 x

Maximum (- 1, 13), Minimum (4, - 112)

Solution steps

f^{'} (x) = 6 x^{2} - 18 x - 24

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 1

into

2 x^{3} - 9 x^{2} - 24 x : 13

Maximum (- 1, 13)

Plug

x = 4

into

2 x^{3} - 9 x^{2} - 24 x : - 112

Minimum (4, - 112)

Maximum (- 1, 13), Minimum (4, - 112)

What is the extreme f(x)=2x^3-9x^2-24x ?
The extreme f(x)=2x^3-9x^2-24x is Maximum(-1,13),Minimum(4,-112)